# Cross Price and Income Elasticity of Demand | CFA Level I Economics

Welcome back! In this lesson, we’ll explore two more types of elasticities: the cross-price elasticity of demand and the income elasticity of demand. Let’s dive right in.

## Adding Variables to the Demand Function

In our previous lesson, we learned about own-price elasticity of demand, demand function, and elasticity coefficient. Now, we will add two more independent variables to the demand function: the **price of related goods** and consumers’ **income** **levels**. We can use their coefficients to calculate the cross-price elasticity of demand and income elasticity of demand.

## Cross-Price Elasticity of Demand

Related goods can be either substitutes or complements. The cross-price elasticity of demand measures the percentage change in quantity demanded for every percentage change in the price of the related good.

**Substitutes:**When the price of a substitute increases, the demand for the good increases, and vice versa. The cross-price elasticity is positive for substitutes.**Complements:**When the price of a complement increases, the demand for the good decreases, and vice versa. The cross-price elasticity is negative for complements.

The more positive the cross-price elasticity, the stronger the substitutionary relationship. Likewise, the more negative the cross-price elasticity, the stronger the complementary relationship.

## Income Elasticity of Demand

When a consumer’s income increases, they can purchase more. However, this doesn’t necessarily mean that the demand for any good will increase. It depends on the type of good:

**Normal goods:** The demand for normal goods increases with consumer income levels, and vice versa. The income elasticity is positive for normal goods.

**Inferior goods:** The demand for inferior goods decreases with consumer income levels. The income elasticity is negative for inferior goods.

## Understanding Elasticity: A McDonald’s Example

We’ll explore an example of elasticity in the context of McDonald’s to help illustrate the concepts of own-price elasticity, cross-price elasticity, and income elasticity of demand.

### McDonald’s Demand Function

Consider the following demand function for a Big Mac at McDonald’s, based on its own price (P_{mac}), the cross-price of a Whopper at Burger King (P_{whopper}), the cross-price of French fries at McDonald’s (P_{fries}), and the income level of a low-income family (I):

**Q _{mac} = 20 – 7P_{mac} + 1.5P_{whopper} – 0.5P_{fries} + 0.004I**

By examining the coefficients of the various factors, we can deduce that a Whopper is a substitute good, French fries are a complementary good, and because the coefficient for the income level is positive, Big Macs are considered normal goods for a low-income family.

### Calculating Elasticities and Consumption

Let’s assume the following prices and income levels:

- Big Mac: $3
- Whopper: $4
- French fries: $2
- Average low-income family’s monthly income: $3,000

Using the demand function, we can calculate the monthly consumption of Big Macs for the low-income family:

**Q _{mac} = 20 – 7(3) + 1.5(4) – 0.5(2) + 0.004(3000) = 16 Big Macs**

Now, let’s examine the various elasticities of demand at this consumption level:

Own-price elasticity = -7 * (3 / 16) = -1.31

Cross-price elasticity (Whopper) = 1.5 * (4 / 16) = 0.375

Cross-price elasticity (French fries) = -0.5 * (2 / 16) = -0.0625

Income elasticity = 0.004 * (3,000 / 16) = 0.75

## Implications for McDonald’s

Among these four factors, the own-price elasticity of demand has the highest absolute value (-1.31), indicating that the demand for Big Macs from low-income families is most sensitive to the price of the Big Mac itself. The other elasticities have absolute values less than 1, which means they are inelastic.

If McDonald’s wants to target low-income families, the most effective approach would be to lower the price of the Big Mac or offer special discount coupons to this demographic. This is because the demand is highly sensitive to the price of the Big Mac itself, and any changes in its price will have a significant impact

**EXAMPLE**

**The demand function for E-scooters in a city is as follows:**

**Q(escooter) = 12,000 – 6P(own) + 2P(ebike) + 0.02I**

**If the price of an E-scooter is $500, the price of an E-bike is $1,200, and the average monthly income is $8,000, calculate the cross-price elasticity of demand for E-scooters against E-bikes and the income elasticity of demand for E-scooters. State whether demand is elastic or inelastic at this level of output.**

**Answer:**

First, calculate the output level of E-scooters based on the given figures:**Q = 12,000 – 6(500) + 2(1,200) + 0.02(8,000) = 11,560 units**

Next, calculate the cross-price elasticity with E-bikes:**Cross-price elasticity = (2 * 1,200) / 11,560 = 0.207**

This means that for every 1% increase in the price of E-bikes, the demand for E-scooters increases by 0.2%.

Finally, calculate the income elasticity:**Income elasticity = (0.02 * 8,000) / 11,560 = 0.014**

This means that for every 1% increase in income level, the demand for E-scooters increases by 0.01%.

As the absolute values of both elasticities are less than 1, both are inelastic at this level of output.

That concludes this lesson on cross-price elasticity and income elasticity. Join us in the next lesson, where we’ll learn to distinguish between the substitution effect and income effect. See you then!

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